POP Steering parameterization

Eddy diffusivity implementation by Bates, Tulloch, Marshall, and Ferrari

Steering Sensitivity Experiments 023,024,025 (alpha,b1,gamma)

This is a suite of sensitivity experiments testing the sensitivity of alpha, gamma and b1.

Experiment 23:

alpha = 8; gamma = 0.8; b1 = 4
/glade/u/home/jet/cases/g.e11.GIAF.T62_gx1v6.steer.023

Experiment 24:

alpha = 8; gamma = 0.8; b1 = 1
/glade/u/home/jet/cases/g.e11.GIAF.T62_gx1v6.steer.024

Experiment 25:

alpha = 8; gamma = 0.35; b1 = 1
/glade/u/home/jet/cases/g.e11.GIAF.T62_gx1v6.steer.025

Notes:

  • In our simulations, we use gamma = 1.75. If we stick with the definition of gamma given in the Appendix of Bates et al. (2014), gamma represents mixing efficiency and cannot exceed 1. However, we can interpret it as const * gamma where we have introduced a scaling constant (const).

  • There is also some very sensitive relationship between b1 and gamma as shown in the paragraph just below A6b.

POP standard diagnostics for the experiments

Experiment 23:

Experiment 24:

Experiment 25:

Comparison of Relavant fields

The fields which are affected by alpha, b1 and gamma are:

  • \(u_{rms} = alpha*{\sigma_{vi}}*L_{eddy}\)

  • \(u_{rms}^2\)

  • \({(U-c)}^2 \over {u_{rms}^2}\)

  • \({Suppression \quad factor = {1 \over (1 + b1 * |\bar u - c|^2 /u_{rms (z=0)}^2 )}}\)

  • \({K}=u_{rms}∗{\Gamma * L_{eddy} \over (1 + b1 * |u_{mean} - c|^2 /u_{rms}^2 (z=0)}\)

\(\color{green}{Comparing \quad RMS \quad eddy \quad velocity}\quad \color{red}{u_{rms}}\)

NOTES:

Alpha was changed to 8.0 for all three sensitivity experiments. It will be compared to the 018 control run and Bate's et al.

  • \(u_{rms} = alpha*{\sigma_{vi}}*L_{eddy}\)

  • alpha (scaling constant) = 8

  • \(\sigma_{vi} = {f \over \sqrt{R_i}}\quad = \quad {f \over \sqrt{{f^2N^2 \over m^4}}}\quad = \quad {{\cancel f m^2} \over \cancel f N}\)

  • \(u_{rms}\) is limited to 5 cm/s $ max(u_{rms},5.)$

\(\quad\quad\quad\quad\quad\quad\quad\) Eddy Velocity \((u_{rms})\quad\) CESM

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\(\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad u_{rms} \) Bates et al

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\(\color{green}{u_{rms}^2 \quad Term} \quad\)

NOTES:

  • \(K={u_{rms}}∗{\Gamma * L_{eddy} \over (1 + b1 * |u_{mean} - c|^2 /\color{red}{u_{rms}^2} (z=0)} \)
  • \(u_{rms}^2\) is a surface value
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\(\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad u_{rms}^2 \) Bates et al

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\(\quad\quad\quad\quad\quad\quad\) \({(U-c)}^2 \over {u_{rms}^2} \quad\) CESM

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\(\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad {|u-c|^2 \over u_{rms}^2} \) Bates et al

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\(\color{green}{\quad Suppression \quad factor = {1 \over (1 + b1 * |\bar u - c|^2 /u_{rms (z=0)}^2 )}}\)

NOTES:

  • \(c = max(- \beta * L_{eddy}^2,-20)\)
  • \(u_{rms} = max(u_{rms},5.)\)
  • \(u_{rms}^2\) is a surface value
  • \(b1\) (scaling constant) = 4. (case23) , 1. (case24), or 1. (case25)

\(\quad\quad\quad\quad\quad\quad\quad\) Suppression Factor CESM

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\(\quad\quad\quad\quad\quad\quad\quad\) Suppression Factor Bates

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\(\quad\quad\quad\quad\quad\quad\quad\) Suppression Factor (Zonal x depth) CESM

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\(\quad\quad\quad\quad\quad\quad\quad\) Suppression Factor (Zonal x depth) Bates

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\(\color{green}{\quad Parameterizing \quad Eddy \quad Diffusivity \quad} (\color{red}{K})\)

NOTES:

  • \(\color{red}{K}=u_{rms}∗{\Gamma * L_{eddy} \over (1 + b1 * |u_{mean} - c|^2 /u_{rms}^2 (z=0)}\)

\(\quad\quad\quad\quad\quad\quad\quad\) Eddy Diffusivity (K) CESM

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\(\quad\quad\quad\quad\quad\quad\quad\) Eddy Diffusivity (K) Bates

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\(\quad\quad\quad\quad\quad\quad\quad\) (Zonal x Depth) CESM

\(\quad\quad\quad\quad\quad\quad\quad\quad\quad\) K limited to (100 < K < 10000)

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Here is the Bate's version

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Posted by John Truesdale